Typically formalization is actually harder than solving a problem. You almost always solve before formalizing. And it can be surprisingly hard to formalize problems that are easy to solve.

For example, is there a polygon of area 100 that you can fit 99 circles of area 1 inside it, without overlapping? Yes, obviously, it's very easy to prove this informally. Now try formalizing it! You will find it takes a while to formalize a number of fairly obvious geometric statements.

The polygon claim is not at all obvious to me, how do you prove it?

Draw 99 circles in a row, then draw a separate polygon around each one with only a teeny amount of excess area, then connect those polygons with teeny little connectors to make it a single polygon. When I say "teeny", you can make those arbitrarily small, so you can certainly fit them under 1 total area.

Okay, it's maybe not "obvious" in a regular human sense, but in a graduate math class you could claim this was "obvious". It would be pretty clear if I were drawing a diagram on a whiteboard. I would definitely take less time proving this to a human, than formalizing it.